Pointwise extensions of GSOS-defined operations

Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on elements of a final coalgebra can be defined by distributive laws (of a syntax Σ functor over a behaviour functor F ). Such distributive laws correspond to abstract specification formats. One such format is a generalization of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ρ that defines operations σ on a final F -coalgebra, we can systematically construct a GSOS specification ρ that defines the pointwise extension σ of σ on a final F-coalgebra. The construction relies on adding a family of auxiliary “buffer” operations to the syntax. These buffer operations depend only on A, and so the construction is uniform for all σ and F .